Multinomial Coefficient Calculator
Discover the number of ways to arrange items into distinct groups. Visualize and understand combinatorics with ease.
Total number of items to arrange.
Comma-separated counts for each group (n1, n2, ... nk).
Multinomial Coefficient:
Visualization of Groups
Visual representation of items distributed into groups.
Understanding Multinomial Coefficient
The multinomial coefficient is a concept in combinatorics that extends the idea of binomial coefficients to more than two categories. It calculates the number of ways to divide a set of n items into k distinct groups of sizes n1, n2, ..., nk, where the sum of group sizes equals n.
It's particularly useful in probability theory, statistics, and various fields of mathematics to count the number of possible arrangements or distributions when items are categorized into multiple groups.
Formula: The multinomial coefficient is given by:
Example: If you have 7 items to divide into 3 groups of sizes 3, 2, and 2, the multinomial coefficient will tell you how many different ways you can form these groups.
This calculator simplifies the process of computing this coefficient, providing both the numerical result and a visual representation of the group distribution.